The large data volume and high algorithm complexity of hyperspectral image (HSI) problems have posed big challenges for efficient classification of massive HSI data repositories. Recently, cloud computing architectures have become more relevant to address the big computational challenges introduced in the HSI field. This article proposes an acceleration method for HSI classification that relies on scheduling metaheuristics to automatically and optimally distribute the workload of HSI applications across multiple computing resources on a cloud platform. By analyzing the procedure of a representative classification method, we first develop its distributed and parallel implementation based on the MapReduce mechanism on Apache Spark. The subtasks of the processing flow that can be processed in a distributed way are identified as divisible tasks. The optimal execution of this application on Spark is further formulated as a divisible scheduling framework that takes into account both task execution precedences and task divisibility when allocating the divisible and indivisible subtasks onto computing nodes. The formulated scheduling framework is an optimization procedure that searches for optimized task assignments and partition counts for divisible tasks. Two metaheuristic algorithms are developed to solve this divisible scheduling problem. The scheduling results provide an optimized solution to the automatic processing of HSI big data on clouds, improving the computational efficiency of HSI classification by exploring the parallelism during the parallel processing flow. Experimental results demonstrate that our scheduling-guided approach achieves remarkable speedups by facilitating the automatic processing of HSI classification on Spark, and is scalable to the increasing HSI data volume.